Question: Solve for $x$ and $y$ using elimination. ${2x+6y = 34}$ ${-2x+5y = -1}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $11y = 33$ $\dfrac{11y}{{11}} = \dfrac{33}{{11}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {2x+6y = 34}\thinspace$ to find $x$ ${2x + 6}{(3)}{= 34}$ $2x+18 = 34$ $2x+18{-18} = 34{-18}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 3}$ into $\thinspace {-2x+5y = -1}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(3)}{= -1}$ ${x = 8}$